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Black can capture the h3 pawn in 6 moves with his king. White doesn't seem to have time to force the black bishop to move, promote the pawn, take the bishiop, take the h4 pawn, move the bishop and push the pawn to h4 to guard it. The only other way would be to force a bishop trade, which I can't see happening either.

Black can capture the h3 pawn in 6 moves with his king. White doesn't seem to have time to force the black bishop to move, promote the pawn, take the bishiop, take the h4 pawn, move the bishop and push the pawn to h4 to guard it. The only other way would be to force a bishop trade, which I can't see happening either.

If black moves away from the queen-side, white king goes to c8, when the black bishop moves away white "closes the door" with Bc7 and then queens. A white king on a8 also wins, the white bishop can force itself into the b8-h2 diagonal by going through a7 then b8.

The only question is if white can force the king away from the queenside. The answer is yes.